Assigned and unassigned distance geometry: applications to biological molecules and nanostructures

Considering geometry based on the concept of distance, the results found by Menger and Blumenthal originated a body of knowledge called distance geometry. This survey covers some recent developments for assigned and unassigned distance geometry and focuses on two main applications: determination of three-dimensional conformations of biological molecules and nanostructures. B Douglas S. Gonçalves [email protected] Simon J. L. Billinge [email protected] Phillip M. Duxbury [email protected] Carlile Lavor [email protected] Antonio Mucherino [email protected] 1 Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA 2 X-ray Scattering Group, Brookhaven National Laboratory, Upton, NY 11973, USA 3 Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA 4 Centro de Ciências Físicas e Matemáticas, Universidade Federal de Santa Catarina, Florianópolis, Brazil 5 Department of Applied Mathematics (IMECC-UNICAMP), University of Campinas, Campinas, SP 13081-970, Brazil 6 Institut de Recherche en Informatique et Systèmes Aléatoires, Université de Rennes 1, 35042 Rennes, France